$5000 @ 2.5% compounded quarterly....what is the total value of the loan in 10 years?

Question

what would be the formula for figuring this out?

Answer 1

5000*[1+(2.5%/4]^(10*4)


5000 * (1.00625)^40

=6,415.13

Answer 2

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RE $5000 @ 2.5% compounded quarterly....what is the total value of the loan in 10 years?

what would be the formula for figuring this out?

Answer 3

I am not sure whether I fully grasp the questions. Is this an installment loan or a balloon note?
If you are asking what will $5,000 be worth in 10 years, growing at 2.5%/year compounded quarterly. The formula is as follows:

A = P x (1 + r/m) ^ (m x t)
A = the value after 10 years
P = Original investment or in your cases $5,000
r = Annual interest rate or in your case .025
m = number of periods per year or in your case 4
t = number of years or in your case 10
^ = means that (m x t) is an exponential or in your case raised to the 40th power.
In you case A = $6,415.13

In an Excel spread sheet you would enter the following:
=FV(r/m,m*t,0,P) or
=FV(.025/4,4*10,5000)

A different question would be if I was making installment payments over 10 years, and I paid them quarterly with a 2.5% interest rate, how much would I totally pay. The answer would be different, because you would be paying part of the original loan back with each payment. The formula is a follows -- I hope you can count parenthesis:

PMT = P / ((1 - (1 / (1 + r/m)^(t*m))) / r/m)
Total Paid = PMT x t x m
In your case, Total Paid = $5,666.54

It can easily be set up in an Excel spreadsheet.

=t*m*PMT(r/m,m*t,P) or
= 10*4*PMT(.025/4,4*10,50000)

Answer 4

Principal * (1+rate)^n
where rate = annual rate/# interest periods per year
n = number of compounding periods

Principal = $5,000.00
annual rate = 2.5%, so rate = 2.5%/4 = .00625
n = 40 (quarterly compounding for 10 years: 4*10=40)

$5,000.00 * (1+.00625)^40 = 6,415.13
$5,000.00 * (1.283027) = 6,415.13

Answer 5

Answer

$6415.11

Formula in Excel

=FV(2.5%/4,10*4,0,5000,1)